SARKARI BAGH, AFGHANISTAN - One recent night, a buried bomb sliced through a hulking military vehicle near here, killing two U.S. soldiers. Last month, the Taliban murdered an Afghan man, stuffed his nose with cash, placed a Koran in his hands and hung his body from a tree. Almost every day, insurgents fire on American troops stationed in this rural village.

Even so, their company commander, Capt. Mikel Resnick, says: "We're winning the war up here."

As a major new offensive gets underway here in the Arghandab River valley and elsewhere in Kandahar province, criticism is rising in Washington about the coherence of the U.S. strategy in Afghanistan. President Obama is said to be troubled by mounting casualties, many in this southern Taliban stronghold. Skeptics in Congress and the White House are demanding more data on the progress of the war.

But the Delta Company soldiers in this one corner of one district have a different view. They arrived two months ago in what was clearly Taliban land. Today it is contested land. To them, violence is a sign of progress: Now the Taliban has someone to fight.

Theirs is, by necessity, a narrow perspective. Mere miles away, the battle is more pitched and the ground more treacherous. Yet, although he does not have charts or graphs to prove it, Resnick, 27, insists that he also sees what the military calls changed "atmospherics": busy stores and streets, tea served to U.S. soldiers. These are glimmers of what commanders say could amount to longer-term success.

"They don't want the Taliban," the battalion commander of troops in the region, Lt. Col. Rodger Lemons, said of Afghans in the valley. "But I think they're still waiting to see what happens."

That assessment highlights the awkward arithmetic behind the influx of U.S. forces into southern Afghanistan, where troops carry the hefty assignment of ejecting the Taliban and linking isolated villagers to local governments. The clock is ticking in Washington midway between Obama's December 2009 troop surge announcement and his July 2011 troop drawdown pledge. But many soldiers have only recently carved bases into remote mountainsides and begun chipping away at a mission they say is difficult but doable.

Encouraging signs

Influential landowners and elders fled as the Taliban presence grew over the last five years in Arghandab, a fertile valley abutting Kandahar city, and many of the few remaining are scared to associate with American troops. Afghan police are widely disliked. Tribal dynamics are opaque, and though Resnick and other commanders took crash courses in Afghan culture, they acknowledge they are not experts.

The part they are experts in - war - is also daunting. The valley's pomegranate orchards and muddy canals make for treacherous terrain that favors insurgents, not U.S. spy planes and tanks. Across the river from the Sarkari Bagh patrol base is a green swath where there is no coalition presence - a perfect escape route for the Taliban that Resnick calls the "wild, wild West."

Still, Resnick and his second-in-command, Capt. Clayton Hendon, 26 - both garrulous former West Point football players - confidently tick off the headway they believe their company has made toward improving security. Soldiers have killed at least a dozen insurgents and suffered zero casualties. Open stores in Sarkari Bagh have quadrupled, and in towns that emptied at the sight of a U.S. soldier two months ago, children swarm and troops sit for tea, they said.

On the day of parliamentary elections in mid-September, a daisy-chain bomb planted in an alley regularly patrolled by soldiers seriously injured a child. But overall there was less violence than Resnick expected.

A tripling of the number of soldiers in this area means that several times a week, Delta Company can patrol orchards that the Taliban roamed freely until this summer and villages where coalition forces had never been before.

But that is where the task - winning trust and connecting people to the government - gets tougher.

On a recent afternoon, a platoon drove on a main road the soldiers call Devil's Alley for its frequent roadside bombs. The destination was Khevejeh Molk, a village the troops considered hostile two months ago and where the Taliban is still powerful enough to have scared off the tribal chief.

The leader of the platoon assigned to the town, 1st Lt. Scott Hendrickson, 31, approached a tailor's shop that symbolized both progress and problems. The suspicious-looking young men who used to hang around had vanished, and the old men inside chatted amiably with Hendrickson, praising the improved security. Then, as if to test him, they asked for solar-powered lights.

"But do it practically!" said one man with a white turban and a glint in his eye. "Not just a promise."

"Tell him the Taliban keep trying to blow up my trucks whenever I come up here," Hendrickson said to his interpreter. "Tell him I need him to help me get rid of the Taliban so I can give him light."

Resnick said a few village elders in his area now feel safe enough to travel 30 minutes south to the district center, which U.S. officials offer as a success story, citing a huge growth in daily visitors, a new court system and a quadrupling of open schools.

The previous district governor was assassinated in June, and most district ministers are too frightened to go to work. But the new district governor, Shah Mohammed, says he is unafraid, and U.S. officials say he is helping to unite the valley's elders.

"You can't really measure energy, but you can feel it," said Chris Harich, a U.S. State Department representative based at the center.

A fatal blast

Up in Delta Company's turf, as in other parts of Arghandab, Taliban "fighting season" - defined by ambushes and shootouts - has given way to a new phase of combat featuring homemade bombs. Military commanders portray this, too, as progress, arguing that it means the Taliban is unwilling to fight face to face.

But it is also a tactic that defines asymmetrical warfare, and it makes bonding with potential Afghan tipsters particularly urgent.

With that and other tasks in mind, a platoon set out on foot one morning from Combat Outpost Sarkari Bagh toward a hamlet that has a friendly tribal chief. 1st Lt. David Burgio, 24, sat on Lal Makhmad's floor, sipping sugary tea and asking Makhmad whether the village might form a community watch. Mahkmad said yes, but only if security improved first, because such a group would invite Taliban wrath.

The conversation continued in a circle. Burgio prodded; Makhmad demurred. Finally, Makhmad agreed that in principle, it could be a good idea.

Burgio counted the visit as a success. The next night, Resnick, sitting with Hendon in their tent office, said such victories were "unconventional, to say the least," but they were adding up.

A few hours later, a low boom sounded in the distance. A bomb clearance convoy based in another district had been struck just a few miles away. A hectic rescue operation ensued from Sarkari Bagh, but two American soldiers could not be saved, and helicopters came to evacuate their bodies and two other soldiers injured in the blast.

The explosion left a 10-foot-deep crater along the main road - close to Makhmad's village. Lemons, the battalion commander, said later that intelligence indicated that the bomb had been tunneled in under the road from an adjacent canal, probably the same day. If true, that might suggest that villagers had done nothing to stop it.

But the morning after the bombing, a red-eyed Resnick said he still felt undeterred. He said he believed the mine might have been a "legacy," or one planted long before the road was paved.

"I never thought I'd have to fly a flag out of here," he said, referring to the U.S. flags that helicopter rescue teams carry with them to cover the bodies of soldiers killed in action. "Or I guess that was my dream."